System and method for reducing peak-to-average ratio (PAR) values

ABSTRACT

A system and method for reducing peak-to-average ratio (PAR) values in signal transmission systems is presented. The presented approach divides a plurality of symbols into a number of non-overlapping subsets of symbols, and manipulates each of the non-overlapping subsets of symbols to produce a plurality of sub-sequences. A strategic manipulation of the subsets of symbols results in the reduction of PAR values.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. provisional patentapplication Ser. No. 60/313,845, filed Aug. 21, 2001, which isincorporated herein by reference in its entirety.

FIELD OF INVENTION

The present invention relates generally to communications systems, and,more particularly, to a system and method for reducing peak-to-averageratio (PAR) values.

BACKGROUND

In modern digital communication, a channel input signal is generallysynthesized as a linear combination of certain bases functions whosecoefficients bear information to be transmitted. For example, in anasymmetric digital subscriber line (ADSL) system using N sub-carriers,the basis function is represented by:

${x(n)} = {\frac{1}{N}{\sum\limits_{k = 0}^{N - 1}\;{{X(k)}{\exp\left( \frac{{j2}\;\pi\;{nk}}{N} \right)}}}}$where X(k) is the coefficient bearing the information symbols to betransmitted. Since the inverse Fourier transform (IFT) is equivalent toa summation of several different frequencies, the resulting signal x(n)becomes approximately Gaussian for large N, according to thecentral-limit theorem. This means that there may be some very high peakspresent in the signal x(n).

One of the problems encountered in the presence of high peaks withinx(n) is a large peak-to-average ratio (PAR) value, or, equivalently, alarge crest factor, which reduces the reliability of transmissionsystems. This is due to the fact that power amplifiers are typicallyonly capable of modulating signals that are bounded by a fixed constant.Thus, any input signal exceeding this value is “clipped” at this level.In other words, if high peaks are present within x(n), then there is apossibility that these high peaks will be “clipped” because the highpeaks exceed the bounds of the power amplifier. This introduces noise tothe system, reduces the signal-to-noise ratio (SNR), and, thus, hasstrong impact on the reliability of the system. In order to reduce thiseffect, one can attenuate the amplitude of the entire signal. However,this worsens the SNR directly, and, further, reduces the system SNR dueto increased quantization noise.

Given the problems associated with potentially large PAR values indigital communication systems, a need exists in the industry to reducePAR values, thereby improving reliability of digital communicationsystems.

SUMMARY

The present invention provides systems and methods for reducingpeak-to-average ratio (PAR) values. Briefly described, in architecture,one embodiment of the system comprises a symbol divider configured todivide a plurality of symbols into a number of non-overlapping subsetsof symbols, and a processor configured to manipulate the subsets ofsymbols to reduce PAR values.

The present invention can also be viewed as providing methods forreducing PAR values. In this regard, one embodiment of the methodcomprises the steps of dividing a plurality of symbols into a number ofnon-overlapping subsets of symbols, and manipulating the non-overlappingsubsets of symbols to reduce the PAR value.

Other systems, methods, features, and advantages of the presentinvention will be or become apparent to one with skill in the art uponexamination of the following drawings and detailed description. It isintended that all such additional systems, methods, features, andadvantages be included within this description, be within the scope ofthe present invention, and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the invention can be better understood with reference tothe following drawings. The components in the drawings are notnecessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the present invention. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 is a block diagram showing a digital communication systememploying asymmetric digital subscriber line (ADSL) technology.

FIG. 2 is a block diagram showing components of the ADSL modem of FIG. 1in greater detail.

FIG. 3A is a graph illustrating an upsampled signal and an interpolatedimpulse response.

FIG. 3B is a graph illustrating an upsampled signal and an interpolatedimpulse response in a high peak-to-average ratio (PAR) value situation.

FIG. 4 is a block diagram showing, in greater detail, a processor in theADSL transceiver unit (ATU) of FIG. 4.

FIG. 5A is a flowchart showing steps associated with one embodiment ofthe invention.

FIG. 5B is a flowchart showing steps associated with another embodimentof the invention.

FIG. 5C is a flowchart showing steps associated with another embodimentof the invention.

FIGS. 6 and 7 are a flowcharts showing additional steps associated oneembodiment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Having summarized various aspects of the present invention, reference isnow made in detail to the description of the embodiments as illustratedin the drawings. While the several embodiments are described inconnection with these drawings, there is no intent to limit theinvention to the embodiment or embodiments disclosed herein. On thecontrary, the intent is to cover all alternatives, modifications, andequivalents included within the spirit and scope of the invention asdefined by the appended claims.

FIG. 1 is a block diagram showing a digital communication system 100. Inthis non-limiting example environment, a central office 110 is connectedto a customer premises 160 via a two-conductor pair wire 155. On theside of the central office 110 an ADSL service rack 140 gathersinformation for transmission. This information may be in the form ofvideo conferencing 115, Internet 120, telephone services 125, movies ondemand 130, or broadcast media 135. All of this information is gatheredat a digital subscriber line access multiplexer (DSLAM) 145, whichassembles the data for transmission by ADSL modems 150. Once thisinformation has been coded and framed, it is sent to the customerpremises 160 via a local loop, which is generally a two-conductor pairwire 155. The data is received at the customer premises 160 by an ADSLmodem 180. This information is then decoded and provided to the user.Several non-limiting examples of this include a fax 165, a user'scomputer 170, a television set 175, an analog telephone 185, or, in thealternative, a digital telephone 195.

FIG. 2 is a block diagram showing an exploded view of the ADSL modems120, 180 at the central office 110 and the customer premises 160 ofFIG. 1. As shown in FIG. 2, the ADSL modem 150 at the central office 110includes an ADSL transceiver unit (ATU-C) 220 that is configured totransmit downstream data and receive upstream data through thetwo-conductor pair wire 155 (also referred to herein as a local loop).On the other end of the local loop 155, at the ADSL modem 180 of thecustomer premises 160, a remote ADSL transceiver unit (ATU-R) 260 isconfigured to receive the downstream data from the ATU-C 220 andtransmit the upstream data from the ATU-R 260 to the ATU-C 220.Typically, the ATU-C 220 sets its gain so that it is high enough tosufficiently satisfy the signal-to-noise ratio (SNR) requirements butnot so high that it results in “clipping” of a signal. Thus, if a spike(or peak) exists in a transmitted signal, then the gain is reduced toaccommodate the spike. This is done at the cost of reducing the SNR ofthe overall signal. Since the PAR value for a Fourier-based system isdefined as:

${{PAR} = \frac{\left( {\max_{i \in {\lbrack{0,{2\;\pi}}\rbrack}}{{p(t)}}} \right)^{2}}{\frac{1}{2\pi}{\int_{0}^{2\pi}{{{p(t)}}^{2}\ {\mathbb{d}t}}}}},$where p(t) represents a signal shape, it can be seen that the PAR valueis large when certain criteria are met. Non-limiting examples ofhigh-PAR value situations are shown in FIGS. 3A and 3B.

FIG. 3A is a graph illustrating an upsampled signal 305 and aninterpolated impulse response 310. Points associated with an impulseresponse are shown in FIG. 3A as shaded circles 360 a, 360 b, 360 c, 360d, 360 e, while the interpolated points are shown as clear circles 365a, 365 b, 365 c, 365 d. Similarly, points associated with the signal areshown in shaded circles 370 a, 370 b, 370 c, 370 d, while the upsampledpoints are shown in clear circles 375 a, 375 b, 375 c, 375 d, 375 e. Thetime interval between the raw data points is represented as T, while thetime interval between the interpolated data points is represented as

$\frac{T}{K}.$For the specific example of FIG. 3A, K is set to 2. As seen here, asignal may have a reasonable negative peak 370 c prior to upsampling.However, a simple upsampling may transform the signal into a high PARvalue signal due to the higher rate filtering (i.e.,

$\frac{T}{K}$filtering). For at least this reason, it is desirable to implement PARvalue reduction techniques on an interpolated signal (i.e., a signalthat has passed through an interpolation filter), rather thanimplementing PAR value reduction techniques on raw signals (i.e.,signals prior to interpolation). One embodiment of a system configuredto reduce PAR values is shown in FIG. 4, and several embodiments ofmethods for reducing PAR values are shown in FIGS. 5A through 7. Thus,details related to reducing PAR values are discussed with reference toFIGS. 4 through 7.

FIG. 3B is a graph illustrating an upsampled signal 305 and aninterpolated impulse response 310 in a boundary condition exhibiting ahigh PAR value. In addition to having potentially high PAR values withina symbol, it is possible to have high boundary values between symbols.Given two adjacent symbols (e.g., a first symbol 330 and a second symbol340 adjacent to the first symbol 330) at a regular sampling rate of T,if:

-   -   (1) a last sample 335 of the first symbol 330 and a first sample        345 of the second symbol 340 have the same sign (i.e., both        positive or both negative);    -   (2) the first sample 345 of the second symbol 340 and the second        sample 350 of the second symbol 340 have different signs (i.e.,        one is positive and the other is negative); and    -   (3) the first sample 345 of the second symbol 340 has a high        magnitude,        then a high PAR value may result due to boundary conditions. One        embodiment of a system for reducing PAR values due to bad        boundary conditions is shown in FIG. 4, and one embodiment of a        method for ameliorating high PAR values due to bad boundary        conditions is shown in FIGS. 5C through 7. Thus, details related        to reducing PAR values due to bad boundary conditions are        discussed with reference to FIGS. 4 through 9.

FIG. 4 is a block diagram showing, in greater detail, a processor 405 inthe ADSL transceiver unit (ATU-C) 220 of FIG. 4. In the specific contextof digital subscriber line (DSL) systems employing discrete multi-tone(DMT) technology, data is transmitted in a plurality of real-valuedsymbols k containing N time samples at a regular sampling rate of

$\frac{1}{T}.$Thus, each symbol may be represented as x_(k)[n], wherein 0≦n≦(N−1). Inother words, the symbol k may be obtained after an N-dimensional inverseFourier transform (IFT) of x_(k)[n]. In one embodiment of the system, asymbol divider 410 in the processor 405 receives a symbol 407 anddivides the symbol 407 into non-overlapping subsets of symbols 412.Thus, the symbol x_(k)[n] is received by the symbol divider 410, andseparated into Q non-overlapping subsets of symbols x_(k) ^((l))[n] suchthat:

${\sum\limits_{i = 1}^{Q}\;\left( {x_{k}^{(l)}\lbrack n\rbrack} \right)} = {{x_{k}\lbrack n\rbrack}.}$Stated differently, the non-overlapping subsets of symbols 412 may bederived using a series of invertible and complete operators O^((l)){ }such that:O ^((l)) {x _(k) [n]}=x _(k) ^((l)) [n],thereby generating a Q-dimensional vector:

${x_{k}\lbrack n\rbrack} = {\begin{bmatrix}{x_{k}^{(1)}\lbrack n\rbrack} \\\ldots \\{x_{k}^{(l)}\lbrack n\rbrack} \\\ldots \\{x_{k}^{(Q)}\lbrack n\rbrack}\end{bmatrix}.}$In a preferred embodiment, the non-overlapping subsets of symbols x_(k)^((l))[n] may be generated so that each subset of symbols x_(k)^((l))[n] is represented by:

${{x_{k}^{(i)}\lbrack n\rbrack} = {\frac{1}{N}2{Re}\left\{ {\sum\limits_{h = 1}^{P_{l}}\;{{\mathbb{e}}^{{j2}\;\pi\frac{{nm}_{h}^{(i)}}{N}}a_{k}^{m_{h}^{(i)}}}} \right\}}},$where a_(k) ^(m) ^(h) ^((l)) is a mapped complex value assigned to binm_(h) ^((l)) for symbol k, based on a bin allocation algorithm. It willbe clear to one of ordinary skill in the art that either uniform ornon-uniform dividing may be applied depending on system constraints. Inany event, the non-overlapping subsets of symbols 412 are received byIFT logic 415, which performs an IFT on each of the non-overlappingsubsets of symbols 412 to produce time-domain subsets 417, which arestored in memory 460 as a Q-dimensional time-domain signal.

The processor 405 also comprises a linear vector generator 422, apattern generator 424, a multiplier 430, and append logic 435. Thelinear vector generator 422 generates Q-dimensional linear vectorse^((m)) 423, which are used to reduce PAR values. In a preferredembodiment, the Q-dimensional linear vectors 423 are binary vectorshaving, as their elements, either 1 or −1. Thus, given that each linearvector 423 is a binary vector having Q elements, there are a total of2^(Q) possible binary vectors that may be generated by the linear vectorgenerator 422. Specifically, if all the elements of the linear vector423 are 1, then the linear vector 423 is designated as a unit vector:

$e^{(1)} = \begin{bmatrix}1 \\\ldots \\1 \\\ldots \\1\end{bmatrix}$such that:e ^((l)T) x _(k) [n]=x _(k) [n].In operation, the linear vector generator 422 generates a Q-dimensionallinear vector e^((m)) 423 and stores the Q-dimensional linear vectore^((m) 423) in memory 630. The multiplier 430 retrieves both the storedQ-dimensional time-domain signal 417 and the stored Q-dimensional linearvector e^((m)) 423, and multiplies the retrieved Q-dimensionaltime-domain signal 417 with the retrieved Q-dimensional linear vectore^((m)) 423, thereby producing a combined sequence. The combinedsequence is stored in memory 460.

The pattern generator 424 generates pattern signals pat^((m))[n] 425,which correspond to the generated linear vectors e^((m)) 423. Thus, forevery linear vector e^((m)) 423, there is a corresponding Q-bit patternsignal pat^((m))[n] 425. In operation, the generated Q-bit patternsignal pat^((m))[n] 425 is stored in memory 460 for use by the appendlogic 435. The append logic 435 retrieves the stored Q-bit patternsignal pat^((m))[n] 425 and the stored combined sequence, and appendsthe Q-bit pattern signal pat^((m))[n] 425 to the combined sequence,thereby producing a patterned sequence y_(k) ^((m)), such that:y _(k) ^((m)) =e ^((m)T) x _(k) [n]+pat ^((m)) [n].As seen here, since there are a total of 2^(Q) linear vectors e^((m))423, a total of 2^(Q) corresponding patterned sequences are generated405.

In one embodiment of the invention, the 2^(Q) combined sequences areupsampled by a resampler 440 to produce interpolated sequences 442.Thus, if the sampling period is given as

$\frac{T}{K},$then the Kn data points in the upsampled sequence {right arrow over(x)}_(k)[Kn−v] are equal to the data points x_(k)[n]. Furthermore, theadditional points {right arrow over (x)}_(k)[Kn+v] due to upsampling areequal to 0 for 1≦v≦(K−1). Thus, if a resampler 440 response at

$\frac{T}{K}$is given as g₁[r], then an upsampling by the resampler 440 results in aninterpolated sequence 442 of:

${{\overset{\sim}{x}}_{k}\lbrack q\rbrack} = {\sum\limits_{r}\;{\left( {{g_{l}\left\lbrack {r\frac{T}{K}} \right\rbrack}{{\overset{\rightharpoonup}{x}}_{k}\left\lbrack {\left( {q - r} \right)\frac{T}{K}} \right\rbrack}} \right).}}$If the interpolated sequence 442 is a result of upsampling the combinedsequence, then this may be represented as {tilde over (y)}_(k)^((m))[q]. As shown here, if the linear vectors e^((m)) 423 are Q-bitvectors, then a total of 2^(Q) sequences of {tilde over (y)}_(k)^((m))[q] are produced, wherein each {tilde over (y)}_(k) ^((m))[q] hasa unique appended pattern signal pat^((m))[n] 425 and corresponds to aunique linear vector e^((m)) 423. In one embodiment of the invention,the PAR for each {tilde over (y)}_(k) ^((m))[q] is calculated by a PARcalculator 445, and the calculated PAR values for {tilde over (y)}_(k)^((m))[q] are stored in memory 460. A comparator 450 retrieves thecalculated PAR values and compares the PAR values in order to determinethe lowest PAR value. Once the lowest PAR value has been determined bythe comparator 450, a correlator 455 correlates the lowest PAR valuewith the linear vector e^((mm)), which corresponds to the lowest PARvalue (also referred to herein as an optimal linear vector e^((mm)). Theoptimal linear vector e^((mm)) is then stored in memory 460. Themultiplier 430 retrieves the Q-dimensional time-domain signal 417 andthe optimal linear vector e^((mm)), and the multiplier 430 multipliesthe Q-dimensional time-domain signal 417 with the transpose of theoptimal linear vector e^((mm)l) to produce an optimal PAR-valuesequence, which is relayed to the append logic 435. The append logic 435retrieves the pattern signal pat^((mm))[n] that corresponds to theoptimal linear vector e^((mm)) and appends pat^((mm))[n] to the optimalPAR-value sequence to produce an optimal patterned sequence {tilde over(y)}_(k) ^((mm))[q]. The optimal patterned sequence is then transmittedby the ATU-C 220.

Since the transmitted sequence has an appended pattern signalpat^((mm))[n], once the sequence has been received at a receive site,the receive site may extract the pattern from the received sequence andreconstruct the sub-sequences using the extracted pattern signalpat^((mm))[n]. Since the sub-sequences are non-overlapping completeportions of the symbol (i.e.,

$\left. {{\sum\limits_{i = 1}^{Q}\;\left( {x_{k}^{(l)}\lbrack n\rbrack} \right)} = {x_{k}\lbrack n\rbrack}} \right),$the reconstructed sub-sequences may simply be concatenated to producethe transmitted symbol. Since the transmitted sequence has beenconfigured to produce the lowest PAR value (i.e., e^((mm)) has beenappropriately chosen), the system as described above may be seen asreducing the PAR value of a transmitted symbol. Further detailsassociated with PAR value reduction are discussed with reference toFIGS. 5A through 7.

While the linear vector e^((mm)) that produces the lowest PAR value maybe useful in reducing PAR values associated with peaks within a symbol,the above sequence may need to be further modified to account forintersymbol interference. In another embodiment of the invention, oncey_(k) ^((m))[n] have been derived, a cyclic prefix of length L may beappended to the beginning of y_(k) ^((m))[n] to account for intersymbolinterference. In this sense, a cyclic prefix is generated by a prefixgenerator 426. The cyclic prefix is appended to y_(k) ^((m))[n] by theappend logic 435, thereby producing a prefixed sequence y_(k) ^((m))[n]for

−L≦n≦(N−1), such that:y _(k) ^((m)′) [n]=y _(k) ^((m)) [n]for 0≦n≦(N−1), andy _(k) ^((m)) [n]=y _(k) ^((m)) [n+N]for −L≦n≦−1.

Once y_(k) ^((m)′)[n] has been derived, the PAR for each y_(k)^((m)′)[n] is calculated by a PAR calculator 445, and the calculated PARvalues for y_(k) ^((m)′)[n] are stored in memory 460. A comparator 450retrieves the calculated PAR values and compares the PAR values todetermine the lowest PAR value. Once the lowest PAR value has beendetermined by the comparator 450, a correlator 455 correlates the lowestPAR value with the linear vector e^((mm)) which corresponds to thelowest PAR value (also referred to herein as an optimal linear vectore^((mm)). The optimal linear vector e^((mm)) is then stored in memory460. The multiplier 430 retrieves the Q-dimensional time-domain signal417 and the optimal linear vector e^((mm)), and the multiplier 430multiplies the Q-dimensional time-domain signal 417 with the transposeof the optimal linear vector e^((mm)T) to produce an optimal PAR-valuesequence, which is relayed to the append logic 435. The append logic 435retrieves the pattern signal pat^((mm))[n] that corresponds to theoptimal linear vector e^((mm)) and appends pat^((mm))[n] to the optimalPAR-value sequence to produce an optimal patterned sequence y_(k)^((mm))[n]. The optimal patterned sequence is then transmitted by theATU-C 220.

Since the transmitted sequence has an appended pattern signalpat^((mm)), and since the appended prefix is cyclic (i.e., duplicativeof the last values of the sequence), once the sequence has been receivedat a receive site, the receive site may reconstruct the sub-sequencesusing the pattern signal pat^((mm))[n] and the known cyclic prefixinformation. Since the sub-sequences are non-overlapping completeportions of the symbol (i.e.,

$\left. {{\sum\limits_{i = 1}^{Q}\;\left( {x_{k}^{(l)}\lbrack n\rbrack} \right)} = {x_{k}\lbrack n\rbrack}} \right),$the reconstructed sub-sequences may simply be concatenated to producethe transmitted symbol. Since the transmitted sequence has beenconfigured to produce the lowest PAR value (i.e., e^((mm)) has beenappropriately chosen), the system as described above may be seen asreducing the PAR value of a transmitted symbol. Further detailsassociated with PAR value reduction are discussed with reference toFIGS. 5A through 7.

While the above sequence may further reduce intersymbol interference, inorder to further reduce large PAR values associated with boundaryconditions, the sequence may need to be further modified. In anotherembodiment of the invention, once prefixed y_(k) ^((m)′)[n] have beenderived, a suffix of length J may be further added to the sequence toaccount for the boundary conditions. In this sense, the suffix isgenerated by a suffix generator 428. The suffix is appended to the endof y_(k) ^((m)′)[n] by the append logic 435, thereby producing asuffixed sequence y_(k) ^((m)″)[n] for −L≦n≦(N+J−1), such that:y _(k) ^((m)″) [n]=y _(k) ^((m)) [n]for 0≦n≦(N−1),y _(k) ^((m)″)[n]=y_(k) ^((m)) [n+N]for −L≦n≦−1, andy _(k) ^((m)″)[n]=s_(k) ^((m)) [n]for N≦n≦(N+J−1). As explained with reference to FIG. 3B, high PAR valuesfor certain boundary conditions arise due to the values of the boundarysamples (i.e., the last sample 335 (FIG. 3B) of the first symbol 330(FIG. 3B), the first sample 345 (FIG. 3B) of the second symbol 340 (FIG.3B), and the second sample 350 (FIG. 3B) of the second symbol 340 (FIG.3B)). Thus, s_(k) ^((m))[n] may be set to compensate for the boundaryconditions by using tuning parameters α and β such that:s _(k) ^((m)) [N]={y _(k) ^((m)) [N−1]}ασwhere σ is the standard deviation of the system, ands _(k) ^((m)) [N+1]=−{y _(k) ^((m)) [N−1]}αβ.These tuning parameters may be derived during initialization, and maydepend on channel characteristics known by both the ATU-C 220 (FIG. 2)and the ATU-R 260 (FIG. 2). Thus, by manipulating the amplitude and signof the values of the boundary samples, the PAR value due to boundaryconditions between symbols may be further reduced.

Once y_(k) ^((m)″)[n] has been derived, the PAR for each y_(k)^((m)″)[n] is calculated by a PAR calculator 445, and the calculated PARvalues for each y_(k) ^((m)″)[n] are stored in memory 460. A comparator450 retrieves the calculated PAR values and compares the PAR values todetermine the lowest PAR value. Once the lowest PAR value has beendetermined by the comparator 450, a correlator 455 correlates the lowestPAR value with the linear vector e^((mm)) that corresponds to the lowestPAR value (hereinafter also referred to as an optimal linear vectore^((mm)). The optimal linear vector e^((mm)) is then stored in memory460. The multiplier 430 retrieves the Q-dimensional time-domain signal417 and the optimal linear vector e^((mm)). The Q-dimensionaltime-domain signal 417 is multiplied by the transpose of the optimallinear vector e^((mm)T) to produce an optimal PAR-value sequence, whichis relayed to the append logic 435. The append logic 435 retrieves thepattern signal pat^((mm))[n] that corresponds to the optimal linearvector e^((mm)) and appends pat^((mm))[n] to the optimal PAR-valuesequence to produce an optimal patterned sequence y_(k) ^((mm)″)[n]. Theoptimal patterned sequence is transmitted by the ATU-C 220.

Since the transmitted sequence has an appended pattern signalpat^((mm))[n], and since the suffix is determined by tuning parametersdetermined during initialization, once the sequence has been received ata receive site, the receive site may reconstruct the sub-sequences usingthe pattern signal pat^((mm))[n] and other known parameters. Since thesub-sequences are non-overlapping complete portions of the symbol (i.e.,

$\left. {{\sum\limits_{i = 1}^{Q}\;\left( {x_{k}^{(l)}\lbrack n\rbrack} \right)} = {x_{k}\lbrack n\rbrack}} \right),$the reconstructed sub-sequences may simply be concatenated to producethe transmitted symbol. Since the transmitted sequence has beenconfigured to produce the lowest PAR value (i.e., e^((mm)) has beenappropriately chosen), the system as described above may be seen asreducing the PAR value of a transmitted symbol. Further detailsassociated with PAR value reduction are discussed with reference toFIGS. 5A through 7.

Having described several embodiments of systems for reducing PAR values,attention is turned to FIGS. 5A through 7, which show severalembodiments of methods for reducing PAR values.

FIG. 5A is a flowchart showing steps 500 a associated with oneembodiment of the invention. As shown in FIG. 5A, one embodiment of themethod begins by dividing, in step 510, a symbol x_(k)[n] into a numberof non-overlapping subsets of symbols x_(k) ^((l))[n]. In oneembodiment, the symbol divider 410 (FIG. 4) may be used to divide 510the symbol x_(k)[n]. Thus, the symbol x_(k)[n] is divided 510 into Qnon-overlapping subsets of symbols x_(k) ^((l))[n] such that:

${\sum\limits_{i = 1}^{Q}\;\left( {x_{k}^{(l)}\lbrack n\rbrack} \right)} = {{x_{k}\lbrack n\rbrack}.}$Stated differently, the non-overlapping subsets of symbols x_(k)^((m))[n] may be derived using a series of invertible and completeoperators O^((l)){ } such that:O ^((l)) {x _(k) [n]}=x _(k) ^((l)) [n],thereby generating a Q-dimensional vector:

${x_{k}\lbrack n\rbrack} = {\begin{bmatrix}{x_{k}^{(l)}\lbrack n\rbrack} \\\cdots \\{x_{k}^{(i)}\lbrack n\rbrack} \\\ldots \\{x_{k}^{(Q)}\lbrack n\rbrack}\end{bmatrix}.}$Once the symbol x_(k)[n] has been divided 510, a linear vector e^((m))is generated, in step 515. In a preferred embodiment, the linear vectore^((m)) is a Q-dimensional binary vector having, as its elements, either1 or −1. Upon generating 515 the linear vector e^((m)), an IFT isperformed, in step 520, on each non-overlapping subset of symbols x_(k)^((l))[n] to produce a plurality of sub-sequences. The plurality ofsub-sequences is then multiplied, in step 525, by the transpose of thelinear vector e^((m)T) to produce a combined sequence. The combinedsequence is upsampled, in step 530, to produce an interpolated sequence{tilde over (y)}_(k) ^((m))[q]. Upon upsampling 530, a PAR value for{tilde over (y)}_(k) ^((m))[q] is calculated, in step 545, and thecalculated 545 PAR value is stored, in step 555. Furthermore, uponupsampling 530, a pattern signal pat^((m))[n] is appended, in step 550,to the interpolated sequence {tilde over (y)}_(k) ^((m))[q] to produce apatterned sequence y_(k) ^((m)), such that:y _(k) ^((m)) =e ^((m)T) x _(k) [n]+pat ^((m)) [n].

Once a patterned sequence y_(k) ^((m)) has been produced and a PAR valuehas been stored 555 for the interpolated sequence, it is determined, instep 560, whether or not a PAR value has been calculated forinterpolated sequences generated by all of the possible linear vectorse^((m)). If the PAR value for all possible interpolated sequences hasnot been calculated, then the process repeats from step 515, whereinanother linear vector e^((m)) is generated. If, on the other hand, PARvalues for all possible linear vectors e^((m)) have been calculated(i.e., 2^(Q) PAR values have been calculated), then the method stepsexit to FIG. 6.

In a preferred embodiment, the method steps of FIG. 5A are performed bythe processor 405 of FIG. 4. However, it will be clear to one ofordinary skill in the art that the method steps may also be performed byother systems.

FIG. 5B is a flowchart showing steps 500 b associated with anotherembodiment of the invention. As shown in FIG. 5B, one embodiment of themethod begins by dividing, in step 510, a symbol x_(k)[n] into a numberof non-overlapping subsets of symbols x_(k) ^((l))[n]. In oneembodiment, the symbol divider 410 (FIG. 4) may be used to divide 510the symbol x_(k)[n]. Thus, the symbol x_(k)[n] is divided 510 into Qnon-overlapping subsets of symbols x_(k) ^((l))[n] such that:

${\sum\limits_{i = 1}^{Q}\;\left( {x_{k}^{(l)}\lbrack n\rbrack} \right)} = {{x_{k}\lbrack n\rbrack}.}$Stated differently, the non-overlapping subsets of symbols x_(k)^((l))[n] may be derived using a series of invertible and completeoperators O^((l)){ } such that:O ^((l)) {x _(k) [n]}=x _(k) ^((l)) [n],thereby generating a Q-dimensional vector:

${x_{k}\lbrack n\rbrack} = {\begin{bmatrix}{x_{k}^{(l)}\lbrack n\rbrack} \\\cdots \\{x_{k}^{(i)}\lbrack n\rbrack} \\\ldots \\{x_{k}^{(Q)}\lbrack n\rbrack}\end{bmatrix}.}$

Once the symbol x_(k)[n] has been divided 510, a linear vector e^((m))is generated, in step 515. In a preferred embodiment, the linear vectore^((m)) is a Q-dimensional binary vector having, as its elements, either1 or −1. Upon generating 515 the linear vector e^((m)), an IFT isperformed, in step 520, on each non-overlapping subset of symbols x_(k)^((l))[n] to produce a plurality of sub-sequences. The plurality ofsub-sequences is then multiplied, in step 525, by the transpose of thelinear vector e^((m)T) to produce a combined sequence. A cyclic prefixis added, in step 532, to the combined sequence to produce a prefixedsequence y_(k) ^((m))[n] for −L≦n≦(N−1), such that:y _(k) ^((m)′)[n]=y_(k) ^((m)) [n]for 0≦n≦(N−1), andy_(k) ^((m)l) [n]=y _(k) ^((m)) [n+N]for −L≦n≦−1. The prefixed sequence y_(λ) ^((m)′)[n] is upsampled, instep 535, to produce an interpolated sequence. Upon upsampling 535, aPAR value for the interpolated sequence is calculated, in step 545, andthe calculated 545 PAR value is stored, in step 555. Furthermore, uponupsampling 535, a pattern signal pat^((m))[n] is appended, in step 550,to the interpolated sequence to produce a patterned sequence. Once apatterned sequence has been produced and a PAR value has been stored 555for the interpolated sequence, it is determined, in step 560, whether ornot a PAR value has been calculated for interpolated sequences generatedby all of the possible linear vectors e^((m)). If the PAR value for allof the possible interpolated sequences has not been calculated, then theprocess repeats from step 515, wherein another linear vector e^((m)) isgenerated. If, on the other hand, PAR values for all possible linearvectors e^((m)) have been calculated (i.e., 2^(Q) PAR values have beencalculated), then the method steps exit to FIG. 6.

In a preferred embodiment, the method steps of FIG. 5B are performed bythe processor 405 of FIG. 4. However, it will be clear to one ofordinary skill in the art that the method steps may also be performed byother systems.

FIG. 5C is a flowchart showing steps 500 c associated with anotherembodiment of the invention. As shown in FIG. 5C, one embodiment of themethod begins by dividing, in step 510, a symbol x_(k)[n] into a numberof non-overlapping subsets of symbols x_(k) ^((l))[n]. In oneembodiment, the symbol divider 410 (FIG. 4) may be used to divide 510the symbol x_(k)[n]. Thus, the symbol x_(k)[n] is divided 510 into Qnon-overlapping subsets of symbols x_(k) ^((l))[n] such that:

${\sum\limits_{i = 1}^{Q}\;\left( {x_{k}^{(l)}\lbrack n\rbrack} \right)} = {{x_{k}\lbrack n\rbrack}.}$Stated differently, the non-overlapping subsets of symbols x_(k)^((l))[n] may be derived using a series of invertible and completeoperators O^((l)){ } such that:O ^((l)) {x _(k) [n]}=c _(k) ^((l)) [n],thereby generating a Q-dimensional vector:

${x_{k}\lbrack n\rbrack} = {\begin{bmatrix}{x_{k}^{(l)}\lbrack n\rbrack} \\\cdots \\{x_{k}^{(i)}\lbrack n\rbrack} \\\ldots \\{x_{k}^{(Q)}\lbrack n\rbrack}\end{bmatrix}.}$

Once the symbol x_(k)[n] has been divided 510, a linear vector e^((m))is generated, in step 515. In a preferred embodiment, the linear vectore^((m)) is a Q-dimensional binary vector having, as its elements, either1 or −1. Upon generating 515 the linear vector e^((m)), an IFT isperformed, in step 520, on each non-overlapping subset of symbols x_(k)^((l))[n] to produce a plurality of sub-sequences. The plurality ofsub-sequences is then multiplied, in step 525, by the transpose of thelinear vector e^((m)T) to produce a combined sequence. A cyclic prefixis added, in step 532, to the combined sequence to produce a prefixedsequence y_(k) ^((m)′)[n] for −L≦n≦(N−1), such that:y _(k) ^((m)′)[n]=y_(k) ^((m)) [n]for 0≦n≦(N−1), andy _(k) ^((m)′) [n]=y _(k) ^((m)) [n+N]for −L≦n≦−1. A suffix is also added, in step 537, to the prefixedsequence to produce a suffixed sequence y_(k) ^((m)″)[n] for−L≦n≦(N+J−1), such that:y _(k) ^((m)″) [n]=y _(k) ^((m)) [n]for 0≦n≦(N−1),y _(k) ^((m)″) [n]=y _(k) ^((m)) [n+N]for −L≦n≦−1, andy _(k) ^((m)″) [n]=s _(k) ^((m)) [n]for N≦n≦(N+J−1). As explained with reference to FIG. 3B, high PAR valuesfor certain boundary conditions arise due to the values of the boundarysamples (i.e., the last sample 335 (FIG. 3B) of the first symbol 330(FIG. 3B), the first sample 345 (FIG. 3B) of the second symbol 340 (FIG.3B), and the second sample 350 (FIG. 3B) of the second symbol 340 (FIG.3B)). Thus, s_(k) ^((m))[n] may be set to compensate for the boundaryconditions by using tuning parameters α and β0 such that:s _(k) ^((m)) [N]={y _(k) ^((m)) [N−1]}ασwhere σ is the standard deviation of the system, ands _(k) ^((m)) [N+1]={y _(k) ^((m)) [N−1]}αβThese tuning parameters may be derived during initialization, and maydepend on channel characteristics known by both the ATU-C 220 (FIG. 2)and the ATU-R 260 (FIG. 2). Thus, by manipulating the amplitude and signof the values of the boundary samples, the PAR value due to boundaryconditions between symbols may be reduced.

The suffixed sequence y_(k) ^((m)″)[n] is upsampled, in step 540, toproduce an interpolated sequence. Upon upsampling 540, a PAR value foreach interpolated sequence is calculated, in step 545, and thecalculated 545 PAR value is stored, in step 555. Furthermore, uponupsampling 540, a pattern signal pat^((m))[n] is appended, in step 550,to the interpolated sequence to produce a patterned sequence. Once apatterned sequence has been produced and a PAR value has been stored 555for the interpolated sequence, it is determined, in step 560, whether ornot a PAR value has been calculated for interpolated sequences generatedby all of the possible linear vectors e^((m)). If the PAR value for allof the possible interpolated sequences has not been calculated, then theprocess repeats from step 515, wherein another linear vector e^((m)) isgenerated. If, on the other hand, PAR values for all possible linearvectors e^((m)) have been calculated (i.e., 2^(Q) PAR values have beencalculated), then the method steps exit to FIG. 6.

In a preferred embodiment, the method steps of FIG. 5C are performed bythe processor 405 of FIG. 4. However, it will be clear to one ofordinary skill in the art that the method steps may also be performed byother systems.

FIGS. 6 and 7 are a flowcharts showing additional steps associated oneembodiment of the invention. Specifically, FIG. 6 completes the datatransmission process in one embodiment of the invention, while FIG. 7addresses the data reception process in one embodiment of the invention.As shown in FIG. 6, once all of the PAR values have been calculated andstored 555, the lowest PAR value is determined, in step 610, from thestored 555 PAR values, and the linear vector corresponding to thedetermined 610 lowest PAR value is ascertained, in step 620. Theascertained 620 linear vector is then transposed and multiplied, in step630, to the sub-sequences to produce an optimal PAR-value sequence, andan optimal pattern corresponding to the ascertained 620 linear vector isgenerated, in step 640. The generated 640 optimal pattern is appended,in step 650, to the optimal PAR-value sequence to produce an optimalpatterned sequence, and the optimal patterned sequence is thentransmitted, in step 660. In a preferred embodiment using ADSL-DMTtechnology, the pattern signal is mapped onto a single tone, such as bin33, so that:

${{{pat}^{(m)}\lbrack n\rbrack} = {2{Re}\left\{ {a_{Q}e^{(m)}{\mathbb{e}}^{{j2}\;\pi\frac{33n}{512}}} \right\}}},$where a_(Q)e^((m)) designates the mapped complex value, which isassociated with the linear vector e^((m)), in a Q-bit quadratureamplitude modulation (QAM) scheme, and Re indicates that the informationis stored in the real portion of the complex number. If a single tone isinsufficient for proper mapping of the pattern signal, then the patternsignal may be mapped onto two tones, such as bin 33 and 34, so that:

${{{pat}^{(m)}\lbrack n\rbrack} = {2{Re}\left\{ {{a_{Q - R}e^{(m)}{\mathbb{e}}^{{j2}\;\pi\frac{33n}{512}}} + {a_{R}e^{(m)}{\mathbb{e}}^{{j2}\;\pi\frac{33n}{512}}}} \right\}}},$where a_(Q-R)e^((m)) and a_(R)e^((m)) designate the mapped complexvalues for the two tones in a QAM scheme.

In a preferred embodiment, the method steps shown in FIG. 6 areperformed by an ATU as shown in FIG. 2. However, it will be clear to oneof ordinary skill in the art that the method steps may also be performedby other systems.

Once the optimal patterned sequence has been transmitted 660, it isreceived, in step 710. In a preferred embodiment of an ADSL-DMT system,since the pattern information is stored on one or two dedicated tones(depending on SNR constraints) as:

${{pat}^{(m)}\lbrack n\rbrack} = {2{Re}\left\{ {a_{Q}e^{(m)}{\mathbb{e}}^{{j2}\;\pi\frac{33n}{512}}} \right\}}$or

${{{pat}^{(m)}\lbrack n\rbrack} = {2{Re}\left\{ {{a_{Q - R}e^{(m)}{\mathbb{e}}^{{j2}\;\pi\frac{33n}{512}}} + {a_{R}e^{(m)}{\mathbb{e}}^{{j2}\;\pi\frac{33n}{512}}}} \right\}}},$the pattern signal is extracted from the dedicated tone (or tones) inthe received sequence. This is done in step 720. Upon extracting 720 thepattern signal, the sub-sequences are reconstructed, in step 730, usingthe extracted 720 pattern signal, thereby producing the desired signal.

The symbol divider 410, IFT logic 415, linear vector generator 422,pattern generator 424, prefix generator 426, suffix generator 428,multiplier 430, append logic 435, resampler 440, PAR calculator 445,comparator 450, and correlator 455 of the present invention can beimplemented in hardware, software, firmware, or a combination thereof.In the preferred embodiment(s), the symbol divider 410, IFT logic 415,linear vector generator 422, pattern generator 424, prefix generator426, suffix generator 428, multiplier 430, append logic 435, resampler440, PAR calculator 445, comparator 450, and correlator 455 areimplemented in hardware using any or a combination of the followingtechnologies, which are all well known in the art: a discrete logiccircuit(s) having logic gates for implementing logic functions upon datasignals, an application specific integrated circuit (ASIC) havingappropriate combinational logic gates, a programmable gate array(s)(PGA), a field programmable gate array (FPGA), etc. In an alternativeembodiment, the symbol divider 410, IFT logic 415, linear vectorgenerator 422, pattern generator 424, prefix generator 426, suffixgenerator 428, multiplier 430, append logic 435, resampler 440, PARcalculator 445, comparator 450, and correlator 455 are implemented insoftware or firmware that is stored in a memory and that is executed bya suitable instruction execution system.

Any process descriptions or blocks in flow charts should be understoodas representing modules, segments, or portions of code which include oneor more executable instructions for implementing specific logicalfunctions or steps in the process, and alternate implementations areincluded within the scope of the preferred embodiment of the presentinvention in which functions may be executed out of order from thatshown or discussed, including substantially concurrently or in reverseorder, depending on the functionality involved, as would be understoodby those reasonably skilled in the art of the present invention.

Although an exemplary embodiment of the present invention has been shownand described, it will be apparent to those of ordinary skill in the artthat a number of changes, modifications, or alterations to the inventionas described may be made, none of which depart from the spirit of thepresent invention. For example, while the processor of FIG. 4 is shownas including a plurality of components, it will be clear to one ofordinary skill in the art that these components may be separatelylocated in the ATU, apart from the processor. Additionally, while thesymbol divider 410 is shown without a connection to the memory 460, itwill be clear to one of ordinary skill in the art that the symboldivider may be connected to memory 460, thereby providing read and writeaccess to memory 460 by the symbol divider 410. Furthermore, while othercomponents (e.g., IFT logic 415, linear vector generator 422, patterngenerator 424, prefix generator 426, suffix generator 428, multiplier430, append logic 435, resampler 440, PAR calculator 445, comparator450, correlator 455, etc.) are shown with a direct connection to memory460, it will be clear to one of ordinary skill in the art that some ofthese connections may be severed without adverse effect to thefunctionality of the invention. All such changes, modifications, andalterations should therefore be seen as within the scope of the presentinvention.

1. In a digital subscriber line (DSL) system employing discretemulti-tone (DMT) technology, wherein a bandwidth is divided into aplurality of discrete symbols, a method for reducing peak-to-averageratio (PAR) values comprising: (a) dividing the plurality of discretesymbols into non-overlapping subsets of symbols, wherein an aggregationof the non-overlapping subsets of symbols produces the plurality ofdiscrete symbols; (b) generating sub-sequences from the non-overlappingsubsets of symbols by performing an inverse Fourier transform (IFT) oneach of the non-overlapping subsets of symbols; (c) combining thegenerated sub-sequences using a binary vector to produce a combinedsequence, wherein the binary vector has a number of elements equal tothe number of sub-sequences, wherein the binary vector is an arrangementof elements, wherein the elements are either +1 or −1; (d) appending apattern signal to the combined sequence to produce a patterned sequence,wherein the pattern signal corresponds to the arrangement of elements inthe binary vector; (e) adding a cyclic prefix to the patterned sequenceto produce a prefixed sequence; (f) adding a suffix to the prefixedsequence to produce a suffixed sequence; (g) upsampling the suffixedsequence to produce an interpolated sequence; (h) calculating apeak-to-average ratio (PAR) value of the interpolated sequence; (i)storing the calculated PAR value of the interpolated sequence; (j)iteratively repeating steps (c) through (i) to produce a plurality ofbinary vectors and a plurality of calculated PAR values, wherein eachiteration uses a binary vector having a different arrangement ofelements, wherein the iteration of steps (c) through (i) terminates whenevery different arrangement of elements has been used to combine thegenerated sub-sequences; (k) determining the lowest PAR value from thecalculated PAR values; (l) selecting an optimal binary vector from theplurality of binary vectors, wherein the optimal binary vector is thebinary vector corresponding to the lowest PAR value; (m) combining thegenerated sub-sequences using the optimal binary vector to produce anoptimal combined sequence; (n) adding a cyclic prefix to the optimalcombined sequence to produce an optimal prefixed sequence; (o) adding asuffix to the optimal prefixed sequence to produce an optimal PARsequence; and (p) transmitting the optimal PAR sequence.
 2. A system forreducing peak-to-average ratio (PAR) values comprising: a symbol dividerconfigured to divide a plurality of symbols into a number ofnon-overlapping subsets of symbols, wherein the aggregation of thenon-overlapping subsets of symbols produces the plurality of symbols;inverse Fourier transform (IFT) logic configured to perform an IFT oneach of the non-overlapping subsets of symbols to produce a plurality ofsub-sequences; linear vector generator configured to generate a linearvector having a number of elements, wherein the number of elements inthe generated linear vector is the same as the number of sub-sequencesin the plurality of sub-sequences; a multiplier configured to multiplythe generated linear vector with the plurality of sub-sequences toproduce a combined sequence; a resampler configured to upsample thecombined sequence to produce an interpolated sequence; PAR calculatorconfigured to calculate the PAR value of the interpolated sequence; aprefix generator configured to generate a cyclic prefix, wherein thecyclic prefix is configured to reduce intersymbol interference, whereinthe values of the cyclic prefix are the end values of the combinedsequence; memory configured to store the calculated PAR value acomparator configured to compare a plurality of stored PAR valueswherein the comparator is further configured to determine a lowest PARvalue from the compared plurality of stored PAR values; a correlatorconfigured to correlate the determined lowest PAR value with a linearvector; a pattern generator configured to generate a pattern indicativeof the linear vector; and append logic configured to append thegenerated pattern to the linear vector.
 3. The system of claim 2,wherein the append logic is further configured to append the cyclicprefix to the beginning of the linear vector.
 4. The system of claim 2,further comprising a suffix generator configured to generate a suffix,wherein the suffix is configured to reduce effects of intersymbolboundary conditions.
 5. The system of claim 4, wherein the append logicis further configured to append the suffix to the end of the linearvector.
 6. A method for reducing peak-to-average ratio (PAR) valuescomprising: (a) dividing a plurality of symbols into a number ofnon-overlapping subsets of symbols, wherein an aggregation of thenon-overlapping subsets of symbols produces the plurality of symbols;(b) performing an inverse Fourier transform (IFT) on each of thenon-overlapping subsets of symbols to produce a plurality ofsub-sequences; (c) multiplying the plurality of sub-sequences with alinear vector having a number of elements to produce a combinedsequence, wherein the number of elements in the linear vector is thesame as the number of sub-sequences; (d) upsampling the combinedsequence to produce an interpolated sequence; (e) calculating thepeak-to-average ratio (PAR) value of the interpolated sequence; (f)appending a pattern signal to interpolated sequence to produce apatterned sequence, wherein the pattern signal is indicative of linearvector; (g) storing the calculated PAR value; and (h) iterativelyrepeating steps (c) through (g) to produce a plurality of stored PARvalues, wherein each iteration uses a different linear vector in thestep of (c) multiplying the plurality of sub-sequences with a linearvector, wherein each of the plurality of stored PAR values correspondsto a different linear vector.
 7. The method of claim 6, furthercomprising: (i) determining the lowest PAR value from the plurality ofstored PAR values.
 8. The method of claim 7, further comprising: (j)ascertaining the linear vector corresponding to the determined lowestPAR value.
 9. The method of claim 7, further comprising: (k) multiplyingthe plurality of sub-sequences with the ascertained linear vector toproduce an optimal PAR-value sequence.
 10. The method of claim 9,further comprising: (l) adding an optimal pattern signal to the optimalPAR-value sequence to produce an optimal patterned sequence, wherein theoptimal pattern signal corresponds to the ascertained linear vector. 11.The method of claim 10, further comprising: (m) transmitting the optimalpatterned sequence.
 12. The method of claim 11, further comprising: (n)receiving the optimal patterned sequence; (o) extracting the patternsignal from the optimal patterned sequence; and (p) reconstructing thesub-sequences using the extracted pattern signal.
 13. The method ofclaim 6, wherein the linear vector is a binary vector.
 14. The method ofclaim 13, wherein each element of the binary vector is either +1 or −1.15. A method for reducing peak-to-average ratio (PAR) values comprising:(a) dividing a plurality of symbols into a number of non-overlappingsubsets of symbols, wherein an aggregation of the non-overlappingsubsets of symbols produces the plurality of symbols; (b) performing aninverse Fourier transform (IFT) on each of the non-overlapping subsetsof symbols to produce a plurality of sub-sequences; (c) multiplying theplurality of sub-sequences with a linear vector having a number ofelements to produce a combined sequence, wherein the number of elementsin the linear vector is the same as the number of sub-sequences; (d)adding a cyclic prefix to the combined sequence to produce a prefixedsequence; (e) upsampling the prefixed sequence to produce aninterpolated sequence; (f) calculating the peak-to-average ratio (PAR)value of the interpolated sequence; (g) appending a pattern signal tothe interpolated sequence to produce a patterned sequence, wherein thepattern signal corresponds to the linear vector; (h) storing thecalculated PAR value; and (i) iteratively repeating steps (c) through(h) to produce a plurality of stored PAR values, wherein each iterationuses a different linear vector in the step of (c) multiplying theplurality of sub-sequences with a linear vector, wherein each of theplurality of stored PAR values corresponds to a different linear vector.16. The method of claim 15, further comprising: (j) determining thelowest PAR value from the plurality of stored PAR values; (k)ascertaining the linear vector corresponding to the determined lowestPAR value; (l) multiplying the plurality of sub-sequences with theascertained linear vector to produce an optimal PAR-value sequence; and(m) adding an optimal pattern signal to the optimal PAR-value sequenceto produce an optimal patterned sequence, wherein the optimal patternsignal corresponds to the ascertained linear vector.
 17. The method ofclaim 15, wherein the cyclic prefix is configured to reduce anintersymbol interference.
 18. The method of claim 15, wherein the valuesof the cyclic prefix are the end values of the combined sequence.
 19. Amethod for reducing peak-to-average ratio (PAR) values comprising: (a)dividing a plurality of symbols into a number of non-overlapping subsetsof symbols, wherein an aggregation of the non-overlapping subsets ofsymbols produces the plurality of symbols; (b) performing an inverseFourier transform (IFT) on each of the non-overlapping subsets ofsymbols to produce a plurality of sub-sequences; (c) multiplying theplurality of sub-sequences with a linear vector having a number ofelements to produce a combined sequence, wherein the number of elementsis the same as the number of sub-sequences; (d) adding a cyclic prefixto the combined sequence to produce a prefixed sequence; (e) adding asuffix to the prefixed sequence to produce a suffixed sequence; (f)upsampling the suffixed sequence to produce an interpolated sequence;(g) calculating the peak-to-average ratio (PAR) value of theinterpolated sequence; (h) appending a pattern signal to theinterpolated sequence to produce a patterned sequence, wherein thepattern signal corresponds to the linear vector; (i) storing thecalculated PAR value; and (j) iteratively repeating steps (c) through(i) to produce a plurality of stored PAR values wherein each iterationuses a different linear vector in the step of (c) multiplying theplurality of sub-sequences with a linear vector wherein each of theplurality of stored PAR values corresponds to a different linear vector.20. The method of claim 19, further comprising: (k) determining thelowest PAR value from the plurality of stored PAR values; (l)ascertaining the linear vector corresponding to the determined lowestPAR value; (m) multiplying the plurality of sub-sequences with theascertained linear vector to produce an optimal PAR-value sequence; and(n) adding an optimal pattern signal to the optimal PAR-value sequenceto produce an optimal patterned sequence, wherein the optimal patternsignal corresponds to the ascertained linear vector.
 21. The method ofclaim 19, wherein the suffix is configured to reduce effects ofintersymbol boundary conditions.
 22. A system for reducingpeak-to-average ratio (PAR) values comprising: (a) means for dividing aplurality of symbols into a number of non-overlapping subsets ofsymbols, wherein an aggregation of the non-overlapping subsets ofsymbols produces the plurality of symbols; (b) means for performing aninverse Fourier transform (IFT) on each of the non-overlapping subsetsof symbols to produce a plurality of sub-sequences; (c) means formultiplying the plurality of sub-sequences with a linear vector having anumber of elements to produce a combined sequence, wherein the number ofelements in the linear vector is the same as the number of sub-sequenceswherein the linear vector is a binary vector wherein each element of thebinary vector is either +1 or −1; (d) means for upsampling the combinedsequence to produce an interpolated sequence; (e) means for calculatingthe peak-to-average ratio (PAR) value of the interpolated sequence; and(f) means for appending a pattern signal to interpolated sequence toproduce a patterned sequence, wherein the pattern signal is indicativeof linear vector; and (g) means for storing the calculated PAR value.23. A system for reducing peak-to-average ratio (PAR) values comprising:(a) means for dividing a plurality of symbols into a number ofnon-overlapping subsets of symbols, wherein an aggregation of thenon-overlapping subsets of symbols produces the plurality of symbols;(b) means for performing an inverse Fourier transform (IFT) on each ofthe non-overlapping subsets of symbols to produce a plurality ofsub-sequences; (c) means for multiplying the plurality of sub-sequenceswith a linear vector having a number of elements to produce a combinedsequence, wherein the number of elements in the linear vector is thesame as the number of sub-sequences; (d) means for adding a cyclicprefix to the combined sequence to produce a prefixed sequence, whereinthe values of the cyclic prefix are the end values of the combinedsequence; (e) means for upsampling the prefixed sequence to produce aninterpolated sequence; (f) means for calculating the peak-to-averageratio (PAR) value of the interpolated sequence; (g) means for appendinga pattern signal to the interpolated sequence to produce a patternedsequence, wherein the pattern signal corresponds to the linear vector;(h) means for storing the calculated PAR value, (i) means fordetermining a lowest PAR value from a plurality of stored PAR values;(j) means for ascertaining a linear vector corresponding to thedetermined lowest PAR value; (k) means for multiplying the plurality ofsub-sequences with the ascertained linear vector to produce an optimalPAR-value sequence; and (l) means for adding an optimal pattern signalto the optimal PAR-value sequence to produce an optimal patternedsequence wherein the optimal pattern signal corresponds to theascertained linear vector.
 24. The system of claim 23, wherein thecyclic prefix is configured to reduce an intersymbol interference.
 25. Asystem for reducing peak-to-average ratio (PAR) values comprising: (a)means for dividing a plurality of symbols into a number ofnon-overlapping subsets of symbols, wherein an aggregation of thenon-overlapping subsets of symbols produces the plurality of symbols;(b) means for performing an inverse Fourier transform (IFT) on each ofthe non-overlapping subsets of symbols to produce a plurality ofsub-sequences; (c) means for multiplying the plurality of sub-sequenceswith a linear vector having a number of elements to produce a combinedsequence, wherein the number of elements is the same as the number ofsub-sequences; (d) means for adding a cyclic prefix to the combinedsequence to produce a prefixed sequence; (e) means for adding a suffixto the prefixed sequence to produce a suffixed sequence; (f) means forupsampling the suffixed sequence to produce an interpolated sequence;(g) means for calculating the peak-to-average ratio (PAR) value of theinterpolated sequence; and (h) means for appending a pattern signal tothe interpolated sequence to produce a patterned sequence, wherein thepattern signal corresponds to the linear vector; (i) means for storingthe calculated PAR value; (j) means for determining a lowest PAR valuefrom a plurality of stored PAR values; (k) means for ascertaining alinear vector corresponding to the determined lowest PAR value; (l)means for multiplying the plurality of sub-sequences with theascertained linear vector to produce an optimal PAR-value sequence; and(m) means for adding an optimal pattern signal to the optimal PAR-valuesequence to produce an optimal patterned sequence wherein the optimalpattern signal corresponds to the ascertained linear vector.
 26. Thesystem of claim 25, wherein the suffix is configured to reduce effectsof intersymbol boundary conditions.